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Addition of Positive and Negative Integers

Introducing a card game that your students can play in small groups to develop their addition skills. This video focuses on addition of positive and negative numbers and briefly touches on subtraction of integers.

This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers and is part of the Math at the Core: Middle School collection.

Materials: Number line with integers from –10 to +10, to be used for demonstration; deck of playing cards—only aces and cards from 2–10, with face cards removed and set aside (Note: You can also use index cards to create 2 sets of 1–10 number cards in red and 2 sets in black); Solving Word Problems activity sheet; for teachers only: Solving Word Problems Answer Key

Procedure: 1. Introduction (5 minutes, whole group)Present the number line to students. Review what integers are when demonstrating the number line. Ask students, What does it mean to add a positive number? (Answer: Adding a positive number on a number line means moving to the right. The value of the number increases because you added to the number.)

Using the number line, demonstrate the increase in value by adding the following:

(–8) + 3 = (–5) and then (–5) + 7 = 2.

Continue to discuss addition and subtraction using the following questions as a guide:

What does it mean to add a negative number? (Answer: Adding a negative number means moving to the left. The value decreases.) Demonstrate with 2 + (–3) = (–1) and –1 + (–3) = (–4).

What happens with subtraction? (Answer: Explain that when we subtract a number, we are actually adding its inverse. So, p – q = p + (–q).)

What does subtracting a positive number mean? (Answer: We move to the left on the number line, in that inverse operation of adding a positive number. The value of the difference is decreased.) Demonstrate on the number line using –4 – 3 = –7 and –7 – 1 = –8.

What does subtracting a negative number mean? (Answer: We move to the right on the number line. The value increases.) Demonstrate using –8 – (–4) = –4 and –4 – (–5) = 1.

2. Integer Card Game Video (5 minutes, whole group)Tell students that they will be playing a card game today. First, they will watch a video to see how the card game works. Show students the video.

3. Integer Card Game Video (15 minutes, small groups)/After the video, distribute playing cards to students seated in groups of three to five and explain the rules of the game:

Have the dealer look through the cards. Only aces and the number cards 2–10 should be used (or use your own cards numbered 1–10).

The dealer shuffles the deck and distributes five cards to each player. Red cards are negative. Black are positive. Players should have a sheet of paper and pencil to record their scores.

For each round, players add (or subtract) the numbers on their cards, confirm this total with the other players, record their scores, and return the cards to the deck.

The dealer then reshuffles the cards and distributes five more to each player.

Play four rounds in the following way:

Rounds 1 and 2: Add the integers.

Rounds 3 and 4: Subtract the integers.

To determine the final score, the dealer shuffles the deck and picks the top card. If it is red, players subtract their resulting numbers from the four rounds. If the card is black, players add their resulting numbers.